Because Bridge CS6 is not supported by Extension Manager anymore, you have to install them manually.
For MXP extension, you can convert it to ZXP extensions with Extension Manager CS6. Then try steps below.
For ZXP extension, use utility software such as 7-zip, WinZip or WinRAR to extract it to a folder.If there is no mxi file after extraction, then it is a CSXS extension.
For CSXS ZXP extension, move the folder to following folder.
Windows: "C:\Program Files (x86)\Common Files\Adobe\CS6ServiceManager\extensions\"
Mac: "/Library/Application Support/Adobe/CS6ServiceManager/extensions/"
For non-CSXS ZXP extension, check the content of the MXI file. Copy all source files defined in "..." to the corresponding destination folders manually. If you are not sure where these files should be copied, please paste the mxi file here.